Back to EveryPatent.com
United States Patent |
6,253,155
|
Hagiwara
|
June 26, 2001
|
Enhanced vertical resolution for logging tools using walsh-transform
deconvolution
Abstract
A method of processing logs to enhance vertical resolution is disclosed. In
one embodiment the method includes: (a) obtaining a measurement signal
from a sensor tool moving through a borehole; (b) determining a Walsh
deconvolution filter; and (c) integrating a product of the Walsh
deconvolution filter and the measurement signal to obtain an enhanced
measurement signal. The Walsh deconvolution filter may be determined by
obtaining a set of tool basis functions from the convolution of the tool
response function with the set of Walsh basis functions, calculating a
tool response correlation matrix, inverting the tool response correlation
matrix, and finding the sum
##EQU1##
This method may be used for continuous or discrete measurement samples.
This method may also be applied to two-dimensional, or time-decay, logs to
enhance their spatial resolution.
Inventors:
|
Hagiwara; Teruhiko (Houston, TX)
|
Assignee:
|
Halliburton Energy Services, Inc. (Houston, TX)
|
Appl. No.:
|
439629 |
Filed:
|
November 12, 1999 |
Current U.S. Class: |
702/9 |
Intern'l Class: |
G06F 019/00 |
Field of Search: |
702/6-10
324/338,339
367/46,25
73/152.03
|
References Cited
U.S. Patent Documents
4562556 | Dec., 1985 | Ingram et al. | 702/6.
|
5227972 | Jul., 1993 | Jacobson | 702/8.
|
5329235 | Jul., 1994 | Zhou et al. | 324/338.
|
5506769 | Apr., 1996 | Fu et al. | 702/8.
|
5619411 | Apr., 1997 | Smith | 702/8.
|
6049209 | Apr., 2000 | Xiao et al. | 324/339.
|
Other References
Gadeken, L.L., et al., "The Utility of Combining Smoothing and
Deconvolution in Processing Algorithms for Well Log Data", Nuclear Science
Symposium, Oct. 22-27, 1990, pp. 810-816.
|
Primary Examiner: McElheny, Jr.; Donald E.
Attorney, Agent or Firm: Conley, Rose & Tayon, P.C.
Claims
What is claimed is:
1. A method of processing logs to enhance resolution, wherein the method
comprises:
obtaining a measurement signal from a sensor tool moving through a
borehole;
determining a Walsh deconvolution filter; and
integrating a product of the Walsh deconvolution filter and the measurement
signal to obtain a measurement signal having an enhanced resolution.
2. The method of claim 1, wherein said measurement signal comprises a set
of measurement samples that corresponds with a set of positions along the
borehole, and wherein said determining a Walsh deconvolution filter
includes:
convolving a tool response of the sensor tool with N Walsh basis functions
W(k,z) to obtain a set of tool basis functions Y(k,z), wherein N is the
number of samples in said set of measurement samples.
3. The method of claim 2, wherein said determining a Walsh deconvolution
filter further includes:
calculating a tool basis correlation matrix Y, wherein the (k,l) element of
Y is
.intg.Y(k;z)Y(l;z)dz.
4. The method of claim 3, wherein said determining a Walsh deconvolution
filter further includes:
inverting the tool basis correlation matrix Y.
5. The method of claim 4, wherein before inverting the tool basis
correlation matrix, said determining a Walsh deconvolution filter further
includes:
modifying the tool basis correlation matrix Y by adding a regularization
parameter .epsilon.I.
6. The method of claim 4, wherein said determining a Walsh deconvolution
filter further includes:
calculating
##EQU10##
where Y.sup.-1 (k,l) is the (k,l) element of the inverted tool basis
correlation matrix Y.sup.-1.
7. The method of claim 1, wherein said integrating is expressible as:
R(z)=.intg.F(z;z')L(z')dz', where F(z;z') represents the Walsh
deconvolution filter, L(z') represents the measurement signal, and R(z)
represents the enhanced measurement signal.
8. A method for enhancing the resolution of logging tool measurements,
wherein the method comprises:
retrieving a set of measurement samples taken at a corresponding set of
positions;
multiplying the set of measurement samples by a Walsh deconvolution filter
to obtain a product; and
integrating the product over the set of positions to obtain a set of
enhanced measurements.
9. The method of claim 8, further comprising:
calculating said Walsh deconvolution filter.
10. The method of claim 9, wherein said calculating includes:
convolving a logging tool response function with a set of Walsh basis
functions W(k,z) to obtain a set of tool basis functions Y(k,z).
11. The method of claim 10, wherein said calculating further includes:
computing a tool basis correlation matrix Y, wherein the (k,l) element of Y
is
##EQU11##
12. The method of claim 9, wherein said calculating includes:
inverting a tool basis correlation matrix Y.
13. The method of claim 12, wherein before said inverting, said calculating
further includes:
adding of a regularization parameter .epsilon.I to said tool basis
correlation matrix Y.
14. The method of claim 12, wherein said calculating further includes:
solving
##EQU12##
where Y.sup.-1 (k,l) is the (k,l) element of the inverted tool basis
correlation matrix Y.sup.-1.
15. The method of claim 8, wherein said integrating is expressible as:
##EQU13##
where F(i;j) represents the Walsh deconvolution filter, L(j) represents
the set of measurement samples, and R(i) represents the set of enhanced
measurement samples.
16. A method for enhancing the spatial resolution of two-dimensional logs,
wherein the method comprises:
for each spatial position in a set of spatial positions, retrieving a
corresponding set of measurement samples taken as a function of time at
that spatial position;
deriving a plurality of samples that share a common time index from said
measurement samples, wherein said plurality includes a sample for each
spatial position in the set of spatial positions;
multiplying the plurality of samples by a Walsh deconvolution filter to
obtain a product; and integrating the product over the set of spatial
positions to obtain a set of enhanced measurements.
17. The method of claim 16, further comprising: repeating said deriving,
multiplying, and integrating for each of a set of time indices to obtain a
corresponding set of enhanced measurements for each time index.
18. The method of claim 16, wherein said deriving includes:
determining a T2 distribution for each set of measurement samples; and
selecting coefficients corresponding to a selected value of T2.
19. The method of claim 16, wherein said deriving includes:
selecting at least one measurement sample from each of the sets of
measurement samples, wherein the selected samples correspond to a time
offset from a measurement trigger performed while a logging tool was
located at a corresponding spatial position.
Description
BACKGROUND OF THE INVENTION
The present invention generally relates to oilfield logging systems, and
more specifically relates to a signal processing method for enhancing
resolution of logging tool measurements.
Modern petroleum drilling and production operations demand a great quantity
of information relating to parameters and conditions downhole. Such
information typically includes characteristics of the earth formations
traversed by the wellbore, along with data relating to the size and
configuration of the borehole itself. The collection of information
relating to conditions downhole, which commonly is referred to as
"logging", can be performed by several methods.
In conventional oil well wireline logging, a probe or "sonde" housing
formation sensors is lowered into the borehole after some or all of the
well has been drilled, and is used to determine certain characteristics of
the formations traversed by the borehole. The upper end of the sonde is
attached to a conductive wireline that suspends the sonde in the borehole.
Power is transmitted to the sensors and instrumentation in the sonde
through the conductive wireline. Similarly, the instrumentation in the
sonde communicates information to the surface by electrical signals
transmitted through the wireline. Since the sonde is in direct electrical
contact with the surface installation, the communications delay is
negligible. Accordingly, measurements can be made and communicated in
"real time".
A disadvantage of obtaining downhole measurements via wireline is that the
drilling assembly must be removed or "tipped" from the drilled borehole
before the desired borehole information can be obtained. This can be both
time-consuming and extremely costly, especially in situations where a
substantial portion of the well has been drilled. In this situation,
thousands of feet of tubing may need to be removed and (if offshore)
stacked on the platform. Typically, drilling rigs are rented by the day at
a substantial cost. Consequently, the cost of drilling a well is directly
proportional to the time required to complete the drilling process.
Removing thousands of feet of tubing to insert a wireline logging tool can
be an expensive proposition.
As a result, there has been an increased emphasis on the collection of data
during the drilling process. Collecting and processing data during the
drilling process eliminates the necessity of removing or tripping the
drilling assembly to insert a wireline logging tool. It consequently
allows the driller to make accurate modifications or corrections as needed
to optimize performance while minimizing down time. Designs for measuring
conditions downhole including the movement and location of the drilling
assembly contemporaneously with the drilling of the well have come to be
known as "measurement-while-drilling" techniques, or "MWD". Similar
techniques, concentrating more on the measurement of formation parameters,
commonly have been referred to as "logging while drilling" techniques, or
"LWD". While distinctions between MWD and LWD may exist, the terms MWD and
LWD often are used interchangeably. For the purposes of this disclosure,
the term LWD will be used with the understanding that this term
encompasses both the collection of formation parameters and the collection
of information relating to the movement and position of the drilling
assembly.
A number of techniques have been used for carrying out wireline and/or LWD
measurements. These include, among others, resistivity, permittivity,
magnetic permeability, acoustic speed, nuclear magnetic resonance (NMR),
gamma radiation (GR) and thermal neutron delay (TMD) measurement
techniques. One problem with the logging tools that make these
measurements is a limited vertical resolution. Each tool has a "tool
response" that extends over a measurement region, causing the tool to
provide a measurement that represents a weighted average of material
properties in that region. This averaging effect "smears" the property
measurements, and creates the possibility that fine-resolution features
(e.g. thin beds and sharp boundaries) may be missed.
"Forward Deconvolution" is one technique that enhances tool resolution. In
the forward deconvolution technique, an approximate or estimated model of
the formation is made from the data logs. This model of the formation is
essentially an estimate of the characteristics of the formation. After the
model of the formation is generated, a computer model of the tool response
is used to transform the estimated model of the formation into an
estimated log. This estimated log is then compared with the actual log
data. One or more parameters of the model formation are then adjusted
based on this comparison of the estimated log to the actual log data, a
new estimated log is calculated, a new comparison is made, and the process
repeats. Thus, the forward deconvolution technique iteratively refines the
model formation until the simulated log approximates the actual log. This
technique is extremely computation intensive.
Consequently, existing techniques for enhancing vertical resolution may be
too computationally burdensome, making it infeasible to resolve with
sufficient accuracy thin beds with a thickness less than the vertical
resolution of the logging tool. Thus, present technology may not be able
to adequately detect and measure thin beds that contain retrievable oil or
other retrievable hydrocarbons. A feasible tool or technique is needed to
detect and measure these thin underground layers or beds. Ideally, this
tool or technique could be used with most or all of the pre-existing oil
field technology.
SUMMARY OF THE INVENTION
Accordingly, there is disclosed herein a method of processing logs to
enhance vertical resolution. In one embodiment the method includes: (a)
obtaining a measurement signal from a sensor tool moving through a
borehole; (b) determining a Walsh deconvolution filter; and (c)
integrating a product of the Walsh deconvolution filter and the
measurement signal to obtain a measurement signal having an enhanced
resolution. The Walsh deconvolution filter may be determined by obtaining
a set of tool basis functions from the convolution of the tool response
function with the set of Walsh basis functions, calculating a tool
response correlation matrix, inverting the tool response correlation
matrix, and finding the sum
##EQU2##
This method may be used for continuous or discrete measurement samples.
Thus, the present invention comprises a combination of features and
advantages which enable it to overcome various problems of prior devices.
The various characteristics described above, as well as other features,
will be readily apparent to those skilled in the art upon reading the
following detailed description of the preferred embodiments of the
invention, and by referring to the accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
For a more detailed description of the preferred embodiment of the present
invention, reference will now be made to the accompanying drawings,
wherein:
FIG. 1 shows a wireline logging operation on a well;
FIG. 2 is a graph of an exemplary logging tool response;
FIG. 3 is a graph comparing a formation property model to logging tool
measurements;
FIG. 4 is a graph of a Walsh deconvolution filter function for the logging
tool response of FIG. 2;
FIG. 5 is a graph comparing a first deconvolved logging tool measurement to
the property model and the original logging tool measurement;
FIG. 6 is a graph of the regularized Walsh deconvolution filter used for
FIG. 5;
FIG. 7 is a graph comparing a second deconvolved logging tool measurement
to the property model and the original logging tool measurement;
FIG. 8 is a graph of the regularized Walsh deconvolution filter used for
FIG. 7;
FIG. 9 is a graph comparing a third deconvolved logging tool measurement to
the property model and the original logging tool measurement;
FIG. 10 is a graph of the regularized Walsh deconvolution filter used for
FIG. 9;
FIG. 11 is a graph comparing a fourth deconvolved logging tool measurement
to the property model and the original logging tool measurement;
FIG. 12 is a graph of the regularized Walsh deconvolution filter used for
FIG. 11;
FIG. 13 is a graph of deconvolution error as a function of the
regularization factor; and
FIG. 14 is a flowchart of the Walsh deconvolution method.
While the invention is susceptible to various modifications and alternative
forms, specific embodiments thereof are shown by way of example in the
drawings and will herein be described in detail. It should be understood,
however, that the drawings and detailed description thereto are not
intended to limit the invention to the particular form disclosed, but on
the contrary, the intention is to cover all modifications, equivalents and
alternatives falling within the spirit and scope of the present invention
as defined by the appended claims.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
Turning now to the figures, FIG. 1 shows a well during wireline logging
operations. A drilling platform 102 is equipped with a derrick 104 that
supports a hoist 106. Drilling of oil and gas wells is commonly carried
out by a string of drill pipes connected together by "tool" joints so as
to form a drilling string that is lowered through a rotary table 112 into
a wellbore 114. In FIG. 1, it is assumed that the drilling string has been
temporarily removed from the wellbore 114 to allow a sonde 116 to be
lowered by wireline 118 into the wellbore 114. Typically, the sonde 116 is
lowered to the bottom of the region of interest and subsequently pulled
upward at a constant speed. During the upward trip, the sonde 116 performs
measurements on the formations 119 adjacent to the wellbore as they pass
by. The measurement data is communicated to a logging facility 120 for
storage, processing, and analysis. Logging facility 120 may be provided
with electronic equipment for performing vertical resolution enhancement
signal processing.
FIG. 2 shows an exemplary tool response for a sonde instrument such as a
NMR tool or a TMD tool. The horizontal axis represents distance in the
vertical direction from the center of the tool. The vertical axis
represents sensitivity to measured properties of materials at that
position. A tool having the illustrated response will provide a
measurement that is a straight average of properties of material in a two
foot region centered at the tool location. As shown in FIG. 3, this
averaging effect prevents tool measurements from reflecting sharp changes
that may occur in the formation. The broken line represents the actual
properties (e.g. resistivity) of a hypothetical formation in which the
beds alternate between 0.1 and 0.7. The solid line represents the measured
properties as logged by the tool. The bed thicknesses decrease from 3 ft,
2 ft, 1.5 ft, 1 ft, to 0.5 ft and back up again. Only as the beds approach
and exceed 2 ft do the measured properties approach the actual formation
properties, and in any event, the sharp property transitions are presented
as gradual transitions.
The vertical resolution of these logging tools is dictated by the tool
response, although the tool speed may sometimes become an additional
limiting factor. Nevertheless, because logging samples can be collected at
a finer interval that the tool resolution, it is possible to enhance the
tool resolution by signal processing. For example, formation properties
are typically sampled every 1/2 ft or 1/4, while the tool resolution is
about 2-4 ft for many logging tools. Without enhancement, only one peak
can be observed within an interval shorter than the inherent tool
resolution. With enhancement, the inherent tool resolution can be improved
to a resolution of approximately twice the sampling interval.
The logged properties L(z) are related to the ideal tool response R(z)
(i.e., the actual formation properties) by convolution with the tool
response function h(z):
L(z)=.intg.h(z-z')R(z')dz' (Eqn. 1)
Since the actual formation properties tend to be fairly rectangular in
nature due to the sudden transitions between bed materials, it may be
considered advantageous to represent the actual formation properties using
a Walsh Transform:
##EQU3##
where 0.ltoreq.k<2.sup.m (2.sup.m is chosen to be the smallest power of two
greater than or equal to the number of sampled points in the log), W(k;z)
represents a Walsh function, and a(k) represents the kth Walsh Transform
coefficient. Walsh functions have a constant magnitude over the range of
the log samples, with the kth function having k transitions between the
positive and negative values. The set of Walsh functions are orthonormal;
ie., they have unit energy and they are mutually orthogonal. Further, they
have built-in sharp transitions that may make them more suitable for
representing the ideal tool response.
A substitution of Eqn. 2 into Eqn. 1 yields:
##EQU4##
For convenience, the bracketed term in Eqn. 3 is hereafter represented by
Y(k;z). Given the logged properties L(z), it is desired to determine the
Walsh Transform coefficients a(k) so that the actual formation properties
R(z) may be found using Eqn. 2. To calculate the transform coefficients,
both sides of Eqn. 3 are multiplied by Y(l;z) and integrated over z:
##EQU5##
Eqn. 4 can be re-written in matrix notation using a 2.sup.m -element vector
.lambda. for the integral on the left side of Eqn. 4, a
2.sup.m.times.2.sup.m -element matrix Y for the integral on the right side
of Eqn. 4, and a 2.sup.m -element vector a for the transform coefficients:
.lambda.=aY (Eqn. 5)
and the transform coefficient vector is found by:
a=.lambda.Y.sup.-1 (Eqn. 6)
From Eqn. 6, it may be observed that a specific transform coefficient is:
##EQU6##
Applying Eqn. 7 to Eqn. 2, the actual formation properties can be
expressed:
##EQU7##
or, for economy of expression:
R(z)=.intg.F(z;z')L(z')dz' (Eqn. 9)
Note that for certain tool response functions, the Walsh deconvolution
filter F(z,z') is not well-behaved. For instance, FIG. 4 shows the Walsh
deconvolution filter F(z;z') that corresponds to the tool response of FIG.
2, assuming that log samples are taken at 1ft intervals over a depth range
of -32 ft to +31 ft. The deconvolution filter as a function of (z-z') is
highly oscillatory and its support is not confined. This behavior may be
attributed to the matrix inversion of Eqn. 6, and may be corrected by
adding a small positive value .epsilon. to the diagonal elements of matrix
Y:
a=.lambda.(Y+.epsilon.I).sup.-1 (Eqn. 10)
so that the regularized Walsh deconvolution filter is expressed:
##EQU8##
FIGS. 6, 8, 10 and 12 show the regularized deconvolution filters for
.epsilon.=0.001 , 0.1, 1, and 5, respectively. FIGS. 5, 7, 9, and 11 show
a comparison of the corresponding deconvolved tool responses (dec) with
both the modeled formation (model) and the actual tool response (tool). In
FIG. 5, the deconvolved tool response accurately reflects the sharp
transitions present in the model, but fails to accurately reflect the
property values in the medium and thick beds. In FIG. 7, the situation is
improved relative to FIG. 5. In FIG. 9, however, the accuracy of the
transitions are degrading, and the property values of the thinner beds are
becoming worse. In FIG. 11, the deconvolved tool response shows only a
small improvement relative to the actual tool response. FIG. 13 shows a
graph of error between the deconvolved tool responses and the model
formation properties as a function of .epsilon. and the number of sample
points. The error .delta.(.epsilon.) is defined as
.delta.(.epsilon.)=.intg..vertline.R.sup.Dec (z;.epsilon.)-R.sup.Model
(z).vertline..sup.2 dz (Eqn. 12)
or, in words, the integrated square of the difference between the
deconvolved tool response and the modeled formation. The minimum error
.delta.(.epsilon.) decreases as the number of samples N=2.sup.m increases.
FIG. 13 also appears to indicate that the optimal value of .epsilon. is
proportional to the number of sample points. Further simulations may be
performed to determine the optimal value of .epsilon. over a range of
expected formation types.
FIG. 14 shows a flowchart of the Walsh transformation deconvolution
process. A set of log samples is obtained, and in block 202 is padded with
zeros if necessary to make the number of samples equal to a power of two.
In block 204, a value is chosen for .epsilon. based on the number of
samples and other factors if appropriate. In block 206, the regularized
Walsh deconvolution filter is calculated per Eqn. 11. In block 208, the
log is multiplied element by element by the Walsh deconvolution filter,
and the product is integrated over z' as indicated by Eqn. 9. The result
is the deconvolved log which may be plotted in block 210.
The deconvolution filter may also be applied to two dimensional data. For
example, nuclear magnetic resonance (NMR) tools measure a time decay curve
(aka "echo train") at each sampled position along the borehole. The NMR
tools also possess a non-ideal tool response in the z-direction. An NMR
log may be represented as L(z;t):
L(z;t)=.intg.h(z-z')R(z';t)dz' (Eqn. 13)
The Walsh deconvolution filter may be applied to deconvolve the tool
response to obtain the true echo train at each depth z as:
R.sup.Dec (z;t;.epsilon.)=.intg.F(z,z';.epsilon.)L(z';t)dz' (Eqn. 14)
In an alternate approach where the true response is a T2-distribution
##EQU9##
the deconvolution filter may be applied to the T.sub.2 -distribution
C(z,T.sub.2) inverted (or mapped) from he echo-train data L(z,t) using
standard techniques:
C.sup.Dec (z;T.sub.2 ;.epsilon.)=.intg.F(z,z';.epsilon.)C.sup.Log
(z';T.sub.2)dz' (Eqn. 16)
A new vertical resolution-enhancement method for logging tool responses has
now been disclosed. The method is based on using the Walsh transform of
the vertical formation property profile to obtain a devonvolution filter
for logging tool measurements. In one example where the logging tool has a
2 ft vertical resolution and logging data are sampled at every 1/2 ft
interval, the profile is recovered up to 1 ft resolution. The disclosed
method is readily applied to enhance the vertical resolution of NMR
logging and other logging tools that measure formation properties through
time-decay spectra.
While preferred embodiments of this invention have been shown and
described, modifications thereof can be made by one skilled in the art
without departing from the spirit or teaching of this invention. The
embodiments described herein are exemplary only and are not limiting. Many
variations and modifications of the system and apparatus are possible and
are within the scope of the invention. Accordingly, the scope of
protection is not limited to the embodiments described herein, but is only
limited by the claims that follow, the scope of which shall include all
equivalents of the subject matter of the claims.
Top